Stability bounds on superluminal propagation in active structures

Active materials have shown promise in achieving superluminal group velocities across broad bandwidths, suggesting potential applications in information transport, antennas, and metamaterial cloaks. However, causality imposes a trade-off between bandwidth, velocity, and propagation distance. This study clarifies superluminal propagation in active structures and derives a stability-based bound on these quantities using filter theory. The bound applies to structures of arbitrary complexity and suggests that significant improvements in superluminal bandwidth are practically limited. These findings provide insights into the limitations of superluminal structures based on active media, highlighting constraints on several proposed applications.

Robert Duggan, Hady Moussa, Younes Ra'di, Dimitrios L. Sounas, Andrea Alù